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- Publisher
- Springer Journals
- Copyright
- Copyright © 2008 by Springer Science+Business Media, LLC
- Subject
- Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-007-9026-5
- Publisher site
- See Article on Publisher Site
Abstract
We consider a new way of establishing Navier wall laws. Considering a bounded domain Ω of R N , N =2,3, surrounded by a thin layer Σ ε , along a part Γ 2 of its boundary ∂ Ω, we consider a Navier-Stokes flow in Ω∪ ∂ Ω∪Σ ε with Reynolds’ number of order 1/ ε in Σ ε . Using Γ-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface Γ 2 . We then consider two special cases where we characterize this matrix of measures. As a further application, we consider an optimal control problem within this context.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2008